Related papers: Peano continua with self regenerating fractals

Let $\mathcal{F}$ be a foliation with a "singular" submanifold $B$ on a smooth manifold $M$ and $p:E \to B$ be a regular neighborhood of $B$ in $M$. Under certain "homogeneity" assumptions on $\mathcal{F}$ near $B$ we prove that every leaf…

Using Gottschalk's notion\,---\,weakly locally almost periodic point, we show in this paper that if $f\colon X\rightarrow X$ is a minimal continuous transformation of a compact Hausdorff space $X$ to itself, then for all entourage…

Topological phases of matter have been extensively investigated in solid state materials and classical wave systems with integer dimensions. However, topological states in non-integer dimensions remain largely unexplored. Fractals, being…

Peano partial cubes are the bipartite graphs whose geodesic interval spaces are (closed) join spaces. They are the partial cubes all of whose finite convex subgraphs have a pre-hull number which is at most 1. Special Peano partial cubes are…

This is the second paper in a series on aura topological spaces $(X, \tau, \mathfrak{a})$, where $\mathfrak{a}: X \to \tau$ is a scope function with $x \in \mathfrak{a}(x)$. We study covering and connectivity properties in this setting.…

For a metrizable space $X$ of density $\kappa$, let $PM(X)$ be the space of continuous bounded pseudometrics on $X$ endowed with the uniform convergence topology. In this paper, its topology shall be classified as follows: (i) If $X$ is…

We deal with topological spaces homeomorphic to their respective squares. Primarily, we investigate the existence of large families of such spaces in some subclasses of compact metrizable spaces. As our main result we show that there is a…

Inspired by a recent work of Dias and Tall, we show that a compact indestructible space is sequentially compact. We also prove that a Lindelof Hausdorff indestructible space has the finite derived set property and a compact Hausdorff…

We describe a new method to construct Laplacians on fractals using a Peano curve from the circle onto the fractal, extending an idea that has been used in the case of certain Julia sets. The Peano curve allows us to visualize eigenfunctions…

Let $X_0$ be a smooth projective threefold which is Fano or which has Picard number $1$. Let $\pi :X\rightarrow X_0$ be a finite composition of blowups along smooth centers. We show that for "almost all" of such $X$, if $f\in Aut(X)$ then…

Given a (singular, codimension 1) holomorphic foliation F on a complex projective manifold X, we study the group PsAut(X, F) of pseudo-automorphisms of X which preserve F ; more precisely, we seek sufficient conditions for a finite index…

We call a nonempty subset $A$ of a topological space $X$ finitely non-Urysohn if for every nonempty finite subset $F$ of $A$ and every family $\{U_x:x\in F\}$ of open neighborhoods $U_x$ of $x\in F$, $\cap\{\mathrm{cl}(U_x):x\in…

We prove that every dynamically coherent plaque expansive partially hyperbolic diffeomorphism is topologically stable with respect to the central foliation (in short, {\em plaque topologically stable}). Next, we study partially hyperbolic…

We report a new type of restoration of macroscopic isotropy (homogenization) in fractals with microscopic anisotropy. The phenomenon is observed in various physical setups, including diffusions, random walks, resistor networks, and Gaussian…

Transcendental H\'enon maps are the natural extensions of the well investigated complex polynomial H\'enon maps to the much larger class of holomorphic automorphisms. We prove here that transcendental H\'enon maps always have non-trivial…

The Rauzy fractal is a domain in the two-dimensional plane constructed by the Rauzy substitution, a substitution rule on three letters. The Rauzy fractal has a fractal-like boundary, and the currently known its constructions is not only for…

Given a closed, smooth 4-manifold $X$ and self-diffeomorphism $f$ that is topologically pseudo-isotopic to the identity, we study the question of whether $f$ is moreover smoothly pseudo-isotopic to the identity. If the fundamental group of…

In the present paper, we prove that a topological space admits a functorial Lindel\"ofification if and only if its realcompactification is Lindel\"of. To investigate the functorial Lindel\"ofifiability of a topological space, for each…

We study definably complete locally o-minimal expansions of ordered groups in this paper. A definable continuous function defined on a closed, bounded and definable set behave like a continuous function on a compact set. We demonstrate…

The following is an open problem in topology: Determine whether the Stone-\v{C}ech compactification of a widely-connected space is necessarily an indecomposable continuum. Herein we describe properties of $X$ that are necessary and…